Applications Of The Reductive Perturbation Method And The Darboux Transformation To Solve The Solitary Wave Of Traffic Flow In Optimal Velocity Model

In recent years, many scholars have studied the traffic flow of car following models such astheoretically of the stability condition discussed and nonlinear density wave analysis, and a smallamount of nonlinear partial differential equation (PDE) and single solitary wave solution were given.In this dissertation, by controlling the parameters to get the PDE equation by the reductiveperturbation method in the optimal velocity model of traffic flow, a greater number of equation suchas KdV, mKdV, Burgerss, WBK ones are given, single-soliton solution and multi-soliton solutionsare given by using both the traveling wave method and the Darboux transformation method. Themain contents of this dissertation are as follows:1) The reduced intake of solitary wave method is applied to solve the traffic flow optimalvelocity model solution. Firstly, the stability condition of the model are obtained by using the lineartheory analysis, then approximate transformation method for nonlinear model is given by nonlinearreductive perturbation. When the three parameters are selected with appropriate values, some thefamous equation such as KdV, mKdV, Burgerss and some of the second order nonlinear PDE can beobtained. The solitons of these solutions are solved by traveling wave method.2)Darboux transformation is applied to solve multisoliton solutions for traffic flow optimalvelocity model. By applying reductive perturbation method to the selected KdV, mKdV, Burgersequation from the second order PDE, the traveling wave solution is selected as the initial solution,based on the known Lax pair, the method of Darboux transformation is appled to calculated themultiple soliton solutions.3)The reductive perturbation and Darboux transformation are applied respectively to deriveWBK equation from traffic flow optimal velocity model and the multi soliton solutions. Thereductive perturbation method is improved and applied to traffic flow optimal velocity model. Byselecting appropriate values of parameters, WBK equation are obtained. Multi-soliton solutions areobtained by Darboux transformation method.